Enforcement officers will make random calls and do spot checks, among other things, to ensure that those on the new, stricter stay-home notice comply with the requirements.
Foreigners who flout the rules during the mandatory 14-day stay at home on returning from China will face penalties such as having their long-term passes revoked.
Singaporeans, on the other hand, would be prosecuted under the Infectious Diseases Act. First-time offenders can be fined up to $10,000, jailed for up to six months, or both.
The new measure was announced by National Development Minister Lawrence Wong yesterday, as Singapore reported two new cases, bringing the total infected to 77.
Mr Wong, who co-chairs the multi-ministry coronavirus task force, said the stay-home notice was prompted by the surge in the number of coronavirus cases in Chinese provinces outside of Hubei province, whose capital Wuhan is the epicentre of the virus outbreak.
The move, he added, "will ensure we reduce the number of imported cases coming back from China, and then we can focus our energies on reducing the risk of local transmission of the virus within Singapore".
China now has 12,000 cases outside Hubei province, a rise from 4,000 at the end of last month, he noted.
The stay-home notice, which takes effect at 11:59pm today, will apply to Singaporeans, permanent residents and long-term pass holders.
As for the existing 14-day leave of absence, it will no longer be issued to those with recent travel history to China, outside of Hubei.
Unlike the new notice, it is less stringent, letting those serving it to leave their homes briefly, say, to buy meals or household supplies.
But under the stay-home notice, people cannot leave their homes.
Support, however, will be available for those who need help to get daily necessities, said the Ministry of Health.
Singaporeans, permanent residents and long-term visit pass holders can turn to the People's Association for help, while students can approach their schools or institutions, or the Education Ministry.
Work-pass holders can seek help from their employers or the Manpower Ministry.
The Government will also give employers $100 for each day a worker is serving the notice. The self-employed are eligible for it too. But the allowance is not for those who can telecommute.
Mr Wong said those on the stay-home notice will be free to decide what they want to do at home, but they are discouraged from having visitors.
Their family members are urged to take precautions, such as practising good hygiene practices and social distancing.
On the other hand, those under home quarantine are required to isolate themselves and cannot interact physically with others living under the same roof.
As of yesterday, there were about 1,200 people under quarantine, with 600 at home and the rest in government quarantine facilities. The capacity of these facilities has doubled to 2,000, from a week ago.
• Additional reporting by Rei Kurohi